Category Archives: About Operation Maths

Operation Maths Digital Resources – Quick Start Guide

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Category : About Operation Maths

If you are a new, or relatively new, Operation Maths user, you should definitely check out this quick start guide to the extensive digital resources which accompany the scheme. And, even if you think that you are relatively familiar with the resources, it might still be worth a read, as you are likely to pick up some new tips to help you get the most out of the resources.

Edco Learning

All of the Operation Maths digital resources are accessed via Edco Learning. All new users will have to first register on the Edco Learning site and follow the instructions to verify the account. If you are not familiar with the Edco Learning site, watch the tutorial below.

After login, you are presented with a virtual book shelf of all your available books. If the Operation Maths books for your class(es) are not visible on the virtual bookshelf, click on the Contact Us link at the top of the Edco Learning home page.

HINT: If you find this virtual bookshelf is too “busy” or is taking a while to load, reduce the number of books you can see when it opens by using the drop-down filters at the top of the screen. Your selection will be remembered for the next time you login. You can amend these choices at any time. 

Operation Maths Digital Resources

As there are some small, subtle differences in the way that the resources are organised for the junior end classes and for the senior end classes, they are dealt with separately below.

Digital Resources for Infants to Second Class:

To get an overview of the digital resources available for each week/fortnight start with the Short Term Plan (STP) for that period, in the Teachers Resource Book (TRB); here the various digital activities are briefly listed (see highlighted below). The TRBs to accompany each class level of the Operation Maths schemes are available both in hard copy (free to all adopting schools) and in digital form (accessible via your bookshelf on Edco Learning).

HINT: To find out more about accessing both the Long Term Plans (LTPs) and Short Term Plans (STPs) for Operation Maths, in both hard copy and digital forms, check out this post: Planning for Operation Maths

This overview lists the digital resources available for that fortnight/week, and in each case specifies:

  • the type of digital activity that it is e.g. Create activity, Write-Hide Show video etc (to find out more information about the different types of digital activities read on here)
  • the page of the At School book to which the activity is relevant
  • a brief description of the activity

To get a more detailed description of the specific digital resources for each week, navigate towards the end of the relevant week, again in the TRB. Here, under the subheading Digital resources, each activity relevant to that week will be given again, accompanied by a detailed description of the activity, suggestions for how to use it in class and extension suggestions (see example below).

To open each specific resource, the simplest way is via the digital version of the At School book. In this digital book, navigate to the page to which the activity is relevant (e.g. in both of the two previous images they list the first create activity as being relevant to page 17 of the At School book). On the specified page, there will be a icon visible (see circled in the example below), which acts as an embedded hyperlink i.e. when you click on the icon, it will automatically open the relevant digital resource, in another tab. For instructions/suggestions on how to use this resource refer back to the detailed description in the TRB (as previously shown in the image above).

 

HINT: While there are other ways to access all of the resources and digital activities (eg via the Edco Resources pop-out tab to the right-hand-side of the screen), the way described above can often be the easiest way to open each embedded resource, as the icons are located in exactly the relevant place in the digital books and so saves the teacher time that might have been spent deciding which resource was the most appropriate.

 

Digital Resources for Third to Sixth Class:

One way to get an overview of the digital resources available for each topic is to start with the Short Term Plan (STP) for that topic, in the Teachers Resource Book (TRB); here, the various digital activities are briefly listed (see image below). The TRBs to accompany each class level of the Operation Maths schemes are available both in hard copy (free to all adopting schools) and in digital form (accessible via your bookshelf on Edco Learning).

HINT: To find out more about accessing both the Long Term Plans (LTPs) and Short Term Plans (STPs) for Operation Maths, in both hard copy and digital forms, check out this post: Planning for Operation Maths

This overview lists the digital resources available for that topic, and in each case specifies:

  • the type of digital activity that it is e.g. Create activity, Write-Hide Show video etc (to find out more information about the different types of digital activities read on here)
  • the page of the Pupil’s Book to which the activity is relevant
  • a brief description of the activity

An alternative place to view an overview of the digital resources available for each topic is on the footer of the first page of each chapter in the Pupil’s book (see opposite), as this also provides the same synopsis of the digital resources that are available to use for that chapter.

To get a more detailed description of the specific digital resources for each topic, navigate to the last section of each chapter in the TRB. Here, under the subheading Digital resources (see circled below), each activity relevant to that topic will be given again, accompanied by a detailed description of the activity, suggestions for how to use it in class and extension suggestions.

 

To open each specific digital resource, the simplest way is via the digital version of the Pupils Book. In this digital book, navigate to the page to which the activity is relevant. On the specified page, there will be a icon visible (see circled in the example opposite), which acts as an embedded hyperlink i.e. when you click on the icon, it will automatically open the relevant digital resource, in another tab. For instructions/suggestions on how to use this resource refer back to the detailed description in the TRB (as previously shown in the image above).

 

HINT: While there are other ways to access all of the resources and digital activities (eg via the Edco Resources pop-out tab to the right-hand-side of the screen), the way described above can often be the easiest way to open each embedded resource, as the icons are located in exactly the relevant place in the digital books and so saves the teacher time that might have been spent deciding which resource was the most appropriate.

 

If you are new to Operation Maths, we recommend that you:

  • subscribe to the Operation Maths blog. This will ensure that you don’t miss out on any new post, as they will be emailed directly to you. To subscribe, just enter your email address in the box at the top right-hand side of this page. 
  • like/follow the Edco Primary Maths page on Facebook and/or Twitter to keep up-to-date on all the latest Operation Maths developments

Operation Maths – Digital Resources Overview

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Category : About Operation Maths

New or relatively new to Operation Maths? Want to know more about the various types of digital resources that are available? Read on!

Operation Maths provides an extensive range of digital resources with endless possibilities. These digital resources include:

  • Create activities (each of these is based on one of seven e-Manipulatives)
  • Ready to go activities (also based on the e-Manipulatives, but more structured than Create activities)
  • Write-hide-show videos
  • Maths Around us videos
  • Scratch activities
  • Follow-on weblinks

Create activities

Create activities are based on one of seven e-Manipulatives and can be used as very powerful online, interactive, teacher tools. The create activities are so called because the teacher can open a specific e-Manipulative and choose how to use it to best suit them, their class and the concept at hand. Therefore, teachers can use the e-Manipulatives in any way that they see fit.

Furthermore, there are numerous suggestions for create activities in the Teachers Resources Book (TRB) which show how the e-Manipulatives can be re-used in numerous ways to achieve a countless number of specific learning outcomes. The detailed suggestions for how to use the create activities, can be found under the subheading Digital resources, located towards the end of the listed activities for each relevant week/topic, in the TRB.

HINT: There are not separate, individual create activities per each hyperlink in the digital Pupils or At School book; clicking on a create activity icon will bring you to the starting point of one of the e-Manipulatives. However, within each of the topics in the TRB, there will be separate and specific suggestions given each time.

The full range of Operation Maths e-Manipulatives cover key maths areas:

  • Sorting & Shop e-Manipulative
  • Place Value e-Manipulative
  • 100 Square e-Manipulative
  • Bar Modelling e-Manipulative
  • Counting Stick e-Manipulative
  • Fractions e-Manipulative
  • Clock e-Manipulative

To explore the seven e-Manipulatives in more detail, please read on here.

 

Ready to go activities

Ready to go activities are specific activities, based again on the seven e-Manipulatives, but these are all pre-set and have suggested questions inbuilt on the left-hand side of the screen, that the teacher can click to reveal and hide. This means that the teacher doesn’t have to waste valuable time looking in a separate book for the accompanying questions. These questions can be directed to specific children and/or can be answered on the children on their Operation Maths MWBs, thereby encouraging whole-class participation.

While both are based on the e-Manipulatives, there is a distinct difference between ready to go and create activities. The former are more structured than their create counterparts and, as each ready to go activity is tailored to a specific learning outcome, they will have a specific title e.g. Ready to go 3.5, Ready to go 4.6 etc

HINT: The ready to go activities can also provide the teacher with examples of how each e-Manipulative may be used. Thus, the teacher can use a previous ready to go activity to inspire a create activity or come up with a completely different activity of their own. 

 

Write-Hide-Show videos

These are videos, of the e-Manipulatives in use, that focuses on the teaching method of ‘Write – Hide – Show’ i.e. teacher plays the video and the children respond by answering on their Operation Maths mini white-boards (MWBs), thus ensuring the maximum participation of the children.

These videos provide quick, easy-to-use scenarios and set-ups that engage children and pose meaningful maths questions. They also showcase the flexibility of the e-Manipulatives and provide inspiration for teachers’ own expansions. Take a look at this sample video below:

 

Maths Around Us videos

The series of Maths Around Us videos is full of real-world examples of maths in the environment and provides numerous opportunities for discussion and engagement. Take a look at this sample video below:

 

 

HINT: An advantage of both types of Operation Maths videos is that they have been designed so that the teacher need only press play, since the questions and wait times are all built in, allowing the children to look, listen and respond on their MWBs. This means that, they not only encourage active participation, but they also allow the teacher the opportunity to informally assess the pupils via observation of their responses.

Scratch programming activities (3rd to 6th class)

Not only have these activities been written especially for Operation Maths but Operations Maths is the only maths scheme available currently in Ireland with integrated programming (coding) activities. Each activity is integrated with the Pupils’ Books, comes with step-by-step instructions for teachers and pupils and highlights the connection between maths and coding in an easy-to-follow, visual manner.
The scratch programming activities can again be downloaded via the icons in the pupils books. Teachers or children can access the Scratch software for free online (click here).

Follow-on weblinks

Encourage your pupils to practice maths ideas at home with the useful Follow-on weblinks based on recommended games. Each Follow-on weblink is author-approved and is linked to a specific topic, for a specific class level, in the Pupils’ Book. The weblinks can be printed for children to take home and have fun practicing maths with their parents or guardians. Teachers can also use the weblinks in class as a lesson starter, for consolidation and assessment or, indeed, at any time.

These follow-on weblinks can be downloaded as word documents from Edco Learning:

  • Open the Edco Resources pop-out tab to the right-hand-side of the screen
  • From the menus select your book (eg “Operation Maths 3rd class Pupils Book”) and “Follow-on Weblinks”

And finally….

  • All the digital resources are all completely integrated with the print and eBooks; when viewing the Pupils eBook, the teacher need only click on the specific digital icon on the page to open the resource up in a new window/tab.
  • Nearly all of the digital resources can be used in conjunction with the free mini white-boards, ensuring the maximum participation of the children.
  • As there are numerous ways to use each of the e-Manipulatives, they offer unlimited opportunities for assessment for learning and whole-class participation
  • They have been specially designed to help children to focus on the maths
  • They are user-friendly and approachable with bright, clear colours and layout

Teachers can access all the Operation Maths digital resources through Edco’s dynamic online digital hub, www.edcolearning.ie.

 

If you are new to Operation Maths, we recommend that you:

  • subscribe to the Operation Maths blog. This will ensure that you don’t miss out on any new post, as they will be emailed directly to you. To subscribe, just enter your email address in the box at the top right-hand side of this page. 
  • like/follow the Edco Primary Maths page on Facebook and/or Twitter to keep up-to-date on all the latest Operation Maths developments

Planning for Operation Maths

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Category : About Operation Maths

If you’re an Operation Maths user, then planning is ‘easy, peasy’, since all the plans are already done!

Long Term Plans (Yearly Schemes):

 There is a hard copy of the each Long Term Plans (LTP) in the front of the Teachers Resource Book (TRB) for each class level, that can be photocopied.
 Open the digital ebook version of the TRB (via Edco Learning) to view the Long Term Plans (Yearly Schemes) and click on the hyperlink in the top corner; this will automatically download a word version of the same plan, allowing you to edit/amend/copy as required.

Short Term Plans (Fortnightly/weekly schemes):

 As before, there is a hard copy at the beginning of each topic in the Teachers Resource Book (TRB) for each class level, that can be photocopied and then annotated, ticked etc.


 Furthermore, to access an editable version of these plans, you need only open the digital ebook version of the TRB to view these same plans and click on the hyperlink in the top corner; this will automatically download a word version of the same plan, allowing you to edit/amend/copy as required.
 In addition, for each of the classes from 3rd to 6th there is a single document compilation of all the short term plans (see image below):
– Login to your Edco Learning account;
– Click on Edco Resources tab on right hand side of screen to open
– From the menus select your TRB (eg “Operation Maths 3rd class TRB”) and “Editable Lesson Plans” and then click on “Short Term Plans Overview” (image 4 below).
You can also use this resources tab to access the word version of the Long Term Plan

 

Multi-Class Plans

For Operation Maths 3-6, as well as including a Long Term Plan (Yearly Scheme) for each class level, there is also a second combined LTP in each TRB; in Operation Maths TRB 3 and 4, there is a combined plan for third and fourth class, and likewise in each Operation Maths TRB 5 and 6 (see image below)

 There is a hard copy in the front of the Teachers Resource Book (TRB) for each class level, that can be photocopied.
 To access a word doc of each plan, open the digital ebook version of the TRB to view the Long Term Plans (Yearly Schemes) and click on the hyperlink in the top left hand corner; this word version allows you to edit/amend/copy as required.

While there are no combined multi-class plans in the Operation Maths TRBs for infants to second class, in response to requests for the same, we now have completed the following:
 A LTP for a combined junior & senior infants class
 A LTP for a combined first & second class
 A LTP for a combined second & third class

And just added:

 A LTP for a combined fourth & fifth class

These plans can be downloaded via the links above or they can be downloaded direct from Edco Learning:

– Login to your Edco Learning account;
– Click on Edco Resources tab on right hand side of screen to open
– From the menus select your TRB (eg “Operation Maths 1st class TRB”) and then “Word Document”.

 

 

If you are new to Operation Maths, we recommend that you:

  • subscribe to the Operation Maths blog. This will ensure that you don’t miss out on any new post, as they will be emailed directly to you. To subscribe, just enter your email address in the box at the top right-hand side of this page. 
  • like/follow the Edco Primary Maths page on Facebook and/or Twitter to keep up-to-date on all the latest Operation Maths developments

 

Operation Maths e-Manipulatives

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Category : About Operation Maths

The fully flexible, easy-to-use, online Operation Maths e-Manipulatives (interactive teacher tools and virtual manipulatives) are designed for teacher-led learning and to encourage whole-class participation. This impressive range of e-Manipulatives is optimised for use on an Interactive Whiteboard or a whiteboard with a projector so that teachers get the best results every time. They also facilitate a CPA approach to maths instruction.

The full range of e-Manipulatives cover key maths areas:

  • Sorting & Shop e-Manipulative
  • Place Value e-Manipulative
  • 100 Square e-Manipulative
  • Bar Modelling e-Manipulative
  • Counting Stick e-Manipulative
  • Fractions e-Manipulative
  • Clock e-Manipulative

Let’s explore each of these in more detail.

 

 The Sorting & Shop e-Manipulative allows the teacher to easily drag and drop shapes, animals, fruit, classroom objects, shop items, upper and lowercase letters, and numbers onto a workspace. It can be used blank or with various backgrounds, including frames, sets,  2×2, 5×5 grids etc . Of all the backgrounds, the shop background is particularly useful as it allows the teacher to create a shop scene with price tags, coins and sale tags, which can be used to explore a wide range of mathematical scenarios such as using small amounts of money in infants right up to scenarios involving percentage increase and decrease in the senior classes.

The Place Value e-Manipulative provides a wide range of place value tables which the teacher can use to demonstrate re-grouping. Each place value table contains either base-ten blocks, counters to represent the place value discs that accompany the 3rd-5th books, straws or money, and decimal values are included in a selection of the tables. Two tables may be shown on screen at the same time to facilitate comparisons between numbers. There is also the facility to display up to 5-digit whole numbers, which, in my experience, had not been possible previously as all other interactive manipulatives only extend to 4-digit numbers at most.

The 100 Square e-Manipulative is another extremely versatile tool. It can be used in numbers only, counters only or counters and numbers. You can very easily hide and reveal individual cells, whole sections of the grid or the entire grid.  I have gotten a huge amount of use of out it recently, with first and second classes, using it in numbers only mode, hiding all the numbers and just revealing one number. I then ask the children what number comes after/before this, what numbers is missing above/below etc. This is particularly good to assess the children’s ability to identify numbers around the decuples/decades (ie 30, 40, 50 etc) which are widely recognised as hurdles for many children.

This tool can also be used to model the 100 dots grid (on the inside back cover of Operation Maths 3 and 4) as a means to explore the commutative and distributive properties and the connections between various groups of facts.

The Bar Modelling e-Manipulative allows the teacher to create the bar models used in the text books quickly and easily. Bars can be dragged, dropped and resized and the teacher can change their colour. The teacher can also type and draw freehand on the workspace, making this a very useful resource for demonstrating the strategy of bar modelling

The Counting Stick e-Manipulative replicates the physical counting stick that a teacher might use in the classroom. The teacher can set the starting value and the steps value, and reveal or hide numbers along the counting stick. Decimal and negative numbers may also be shown on the Counting Stick e-Manipulative and two counting sticks can be shown at the same time, in order to compare various numbers.

The teacher can use the Fractions e-Manipulative to present fraction bars (linear models), fraction circles and pizzas (both area models). The teacher can change the fraction that is shown on screen, randomise fractions and hide or show the fraction value, decimal value and percentage value. Two fractions may be shown on screen at the same time.

Analogue and digital clocks are provided with the Clock e-Manipulative. The teacher can choose to show one analogue clock, one digital clock, two analogue clocks, two digital clocks or an analogue and a digital clock at the same time.

 

All of the e-Manipulatives can be used as Ready to go or Create activities

Ready to go activities are already set up within each e-Manipulative with pre-programmed questions that appear on screen, meaning that the teacher doesn’t have to waste time looking in a book for the accompanying questions. The questions can also be answered on the children on their MWBs, thereby encouraging whole-class participation.

Create activities are so called because the teacher can open the e-Manipulatives and choose how to use it to best suit them, their class and the concept at hand. There are suggestions for Create activities printed in the TRB which show how the tools can be re-used in infinite ways to achieve a countless number of specific learning outcomes. And the Ready to go activities themselves will also provide the teachers with examples of how each e-Manipulative may be used.

Write – Hide – Show videos

These are videos of the e-Manipulatives in use that focuses on the teaching method of ‘Write – Hide – Show’. These videos provide quick, easy-to-use scenarios and set-ups that engage children and pose meaningful maths questions. They also showcase the flexibility of the e-Manipulatives and provide inspiration for teachers’ own expansions. Take a look at this sample video below:

 

Teachers can access all of the Operation Maths e-Manipulatives and other digital resources through Edco’s dynamic online digital hub, www.edcolearning.ie.

Maths for June

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Category : About Operation Maths

Hooray! June is nearly here! You can almost smell the summer holidays!

If you’re a user of Operation Maths 3-6 you are quite likely to be finished, or nearly finished your books, as the programme is designed to be completed by the end of May, so as to have it all covered in advance of the standardised testing.

So now, you might find yourself looking for inspiration to fill the maths lessons from now until the end of month. Whether you’re an Operation Maths user or not, look no further than the following ideas.

For Operation Maths users:

If you hadn’t had a chance to dip into these specific features of the Operation Maths programme so far this year then why not try these out now?

  • Let’s Investigate! These sections are the last one or two pages at the end of the Pupils’ Books ( for third to sixth classes) where the focus is on open-ended problems. Some of these are “big” enough to fill a whole lesson, others might become additions to a lesson or be combined to become a lesson. The children could also select which particular investigation(s) they’d like to explore, either as a whole class or with individual groups selecting different investigations, with results to be communicated/presented back to whole class when complete.
  • Early Finishers Photocopiables: These can be found in your Teachers Resource Book (TRB) and can also be  a great way to help deepen the children’s understanding of a topic covered earlier in the year. For 3rd to 6th classes, problem solving is also an integral part of these activities. In the TRBs for Junior Infants to 2nd classes, there are both Early Finishers photocopiables and dedicated problem-solving activities.
  • Maths Around Us: If your class has access to recording devices, why not challenge them to make their own Maths Around Us video based on maths content they covered this year. Watch some of the Operation Maths Maths Around Us videos on www.edcolearning.ie for inspiration.

As mentioned in a previous post, don’t feel under pressure to complete all of the above activities, only just what appeals most to you or is most suited to your class.

For everybody!

  • Change their attitude to maths generally: Most people have this belief that there is such a thing as a maths brain, a belief which Jo Boaler, among others, strongly challenges. In conjunction with her youcubed team at Stanford University, in 2015 they put together resources, videos etc for a Week of Inspirational Maths. Since then their catalogue of resources has grown and includes videos, resources and tasks. There is enough here to keep a class going for an entire month!
  • Take time to problem-solve: often, during the school year, time is at a premium, yet Dan Finkel argues in this TEDx Talk that “allowing children time to struggle” is one of the Five Principles of Extraordinary Math Teaching. So after watching this video, why not present the images he uses to a 5th or 6th class and give them time to “notice and wonder”. The children could use sentence/questions stems like “I notice that…” and ” I wonder why/how/what ….” to get them thinking and discussing. Read on here for more sources of deep and rich problems.
  • Try out a new methodology with your class: It can be a good idea to try out something new in June when there’s less pressure to succeed and you’re familiar with your class, rather than trying out something new in September when you’re trying to get to grips with new class, new books, perhaps new room etc!  One initiative I would wholeheartedly recommend is Number Talks. You could do a number talk with your class aimed at their current level or challenge them to do a number talks session aimed at the class they’ll be in next September.
  • Do a maths project: In the Maths Curriculum Teacher Guidelines (DES, 1999) maths projects are listed as one of the examples of maths problems that we are encouraged to incorporate into our teaching. It can be difficult to include maths projects earlier in the year when the pressure is on to cover the content, making June an ideal time to explore them. For 10 “awesome” ideas, check out this post from the Mashup Math blog. One of the suggested projects, Plan your Dream Vacation, has so much opportunities for real-life maths, costs, budgeting, estimating costs of luggage, time needed to get to the airport, distance from destination to airport etc. And, if a foreign holiday, is not relevant, with a small twist, and access to some online hardware catalogues it could easily become Plan your Dream Bedroom; again lots of real-life maths, costs, budgeting, measuring, dimensions, proportions etc. Or even plan a virtual Road Trip! Research where to start, where to go, how to travel there, what attractions to visit, the costs involved, and how long it would take.
  • Financial Maths: In a similar vein to that of the previous suggestion, the NCETM Primary and Early Years Magazine also has suggestions for projects, the first one again focusing on financial education. Here they have links to a fantastic suite of primary resources for My Money Week (UK), that are also very applicable to children to children in Ireland. To access the resources, you need to set up a free account, which requires email details etc and entering any UK postcode. Once registered and logged in, scroll down to the bottom of the primary resources and click on Start journey; this will start off a series of excellent videos on Max’s Day Out, in which Max is deciding how best he might spend the money that he got for his birthday. The videos are designed in such a way that each one presents two possible options; the viewer selects an option, which automatically brings them to the follow-up video for their choice. There are many other resources also available here that focus on managing money.
  • Revise wise! Ask your class to put together revision materials for their chosen topic from the past school year. They can show their creative side, using a variety of approaches, including digital media, to complete the task. The types of materials produced could include posters, presentations, video tutorials, raps, songs, poems, models, fact sheets and or revision work-sheets. These child-produced materials could be collected and shared with the next cohort of classes.
  • Picture This: Similar to the revision project above, and to the Maths Around Us videos, the children could be allocated maths terminology that they had encountered during the past year, and be tasked to produce images or video that illustrate the terminology. The children could be encouraged to use real world examples, especially from around their homes and local environment.
  • Online Surveys: The children could be asked to survey the other children in their class, by setting up online surveys (eg using Google Forms, Mentimeter etc) and then to collate and present their conclusions and findings, using spreadsheets, graphics (pie chart, and bar graph) and/or slideshows (eg Google Sheets, Google Slides, etc).
  • Calculator Activities: For any sixth class students transitioning to secondary, it can be a good idea to brush-up on calculator skills; secondary teachers may expect them to be relatively comfortable with this piece of technology. That’s said, calculator activities shouldn’t be just about getting through more calculations in a shorter time; the children should be enabled to use the calculator to explore number patterns, more complicated numbers, real life situations, and to gather evidence to support reasoning, such as in this consecutive numbers concept cartoon.
  • Take it outdoors: Another type of maths problem listed in the Teacher Guidelines is maths trails. If the rain stays away for long enough why not get outside and do some maths trails? Or if you teach a more senior class, why not get them to design a maths trail for a junior class based on the school grounds or nearby environment. For more trail ideas read on here.
  • Maths is Magic! There is a lot of mathematics behind magic. You could give the children magic tricks to investigate. Check out this article, again from the NCETM Primary and Early Years Magazine for sites to explore.
  • Break the code: Explore the maths behind codes and code-breaking. You could ask the children to make up their own codes and crack a friend’s. Click here for links to suitable sites.
  • Have a maths game-themed day: Another one of Dan Finkel’s Five Principles of Extraordinary Math Teaching is play. Most games and puzzles are mathematical in nature. Get the children to bring in a favourite game from home, to play in class, that requires mathematical thinking. Alternatively, get them to research a suitable one on the internet.

Operation Maths Quick-start Guide

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Category : About Operation Maths

Using Operation Maths for the first time? Here is a general quick-start guide for teaching the topics.

Operation Maths for Junior Infants to Second Class:

  1. Start with whole class warm-up and oral; see topic-specific suggestions in the Teacher Resource Book (TRB) or choose your own. Follow this with discussion questions (also in TRB).
  2. Pair work, an activity based in the At School book.
  3. Exploration of concrete materials via Maths Stations; again see topic-specific suggestions in the TRB.
  4. Complete relevant activities in At School and At Home books. The introduction of the TRB includes a year plan that lists the relevant pages of each book per topic, along with other details such as strand and strand units. Bearing in mind that Operation Maths is based on a CPA approach, it is envisaged that the child would engage in all the concrete and pictorial activities for the topic before doing the pages in their books.

For more detailed information on managing the content with Junior Infants to Second Class please read on here.

For a quick-start guide to the digital resources, please read on here.

 

Operation Maths for Third Class to Sixth Class:

  • The Teacher’s Resource Book (TRB) for Operation Maths 3-6 is divided into daily sections, each dedicated to a specific learning outcome.
  • Each topic has material for for either five or ten days, depending on whether it is a single/one week topic or double/two week topic. Double topics are indicated on the contents page of each book using an asterisk (*).

Teachers should start with the daily lesson suggestions in the Teacher’s Resource Book (TRB) as follows:

  • Oral and mental starter
  • Discuss and teach provides suggestions on how to achieve the learning outcome.
  • Pupils’ book and/or discovery book: gives the details for the location of the specific questions that reinforce and consolidate the learning outcome(s) covered in the discuss and teach section.
  • Digital Resources will briefly list any relevant digital activities that can be used from the comprehensive suite on edcolearning.ie . These are also referenced in the Pupils’ books as well and, if accessing the digital books, clicking on the hyperlinks in the Pupils Book will open the resource directly from the book (this is actually the easiest way to access the digital resources).
  • Extra exploration: Suggested activity for early finishers.

Pupils’ Book & Discovery Book: Since Operation Maths is based on a CPA approach, the children’s experience of Operation Maths should not be a purely book-based one. That said, when navigating the children’s books, it will follow this general pattern:

  • The topic (be it single or double), starts in the Discovery Book with the Starting Point activity (see example below), which revises familiar topics or sets the scene for new ones. There may often be no other book-based activities for Day 1.

  • Subsequent “days” (excluding the last day of each topic ie day 5 or day 10) may focus on the Pupils book only, or move between the Pupils’ Book and the Discovery Book. On the days when both books are in use, icons are used to indicate when it would be most appropriate to move to the other book (see below)
The icon on the extreme bottom right indicates that the child should complete the companion activities on page 16 of the Discovery Book next. The icon to the left indicates that there is also a linked digital activity for this learning outcome.

When the child has completed the activities in the Discovery Book there is often a similar icon there, redirecting the child back to the Pupils’ Book.

  • Consolidation is the focus of the last day of each topic i.e. day 5 or day 10. The children can complete the Learning Log activity in their Discovery Book either on this day or on the previous evening as a homework activity. They can also complete the topic assessment in
  • their Pupil Assessment book.

For more detailed information on managing the content with Third to Sixth Class please read on here.

For a quick-start guide to the digital resources, please read on here.

 

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Operation Maths Jr Inf-2nd: Managing the content

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Category : About Operation Maths

As outlined in a previous post, Operation Maths 3 – 6 provides fulsome content for the senior classes. The complaints heard about other schemes – that there is simply not enough to do in the senior class books – is definitely not one heard about Operation Maths! At the junior end of Operation Maths – which is the focus of this post – the Teacher Resource Books (TRBs) are the jewels in the crown: the most comprehensive available and jam packed with the ‘how to’ of setting up maths’ stations, differentiation, oral maths, discussion topics, early finisher activities and a comprehensive stand alone problem solving section. And, since this programme is also based on a CPA approach, the TRBs are full of suggestions on how to promote those methodologies in a classroom.

Familiarity with any new programme takes time and time is a very precious commodity for all us teachers. Therefore, in this post I will give you some tips on how to successfully implement the programme in the junior classes – what in today’s game parlance our students might call ‘cheats’!

1. Start from the Teacher Resource Book

Start with the weekly lesson suggestions in the Teachers’ Resource Book (TRB). Typically these will be laid out as follows:

  • A whole class warm-up and oral, designed to consolidate prior learning and lead logically into the lesson that follows. It is suggested that this lasts for 5-10 minutes  each day of the week, depending on content. While there are typically many suggestions here, it is not necessary to do all of them. If you find a starter that works particularly well, you could note this alongside the margin of your TRB, or in the notes section, to highlight it for future use.

The mini whiteboards are invaluable for this part of the lesson. Look out for children who lack the confidence or know how and are hesitant to write their answer or copy others. Encourage a growth mindset:
1. It’s okay to make mistakes, everyone does! We learn from them.
2. Often there is more than one correct approach; eg 17+19 can be modeled/thought of as move one to 19 to become 16 + 20, move 3 to 17 to become 20 +16, move one to 17 to become 18 + 18

  • Discussion questions that stimulate talk and discussion in a relevant and meaningful way. Again, only do as many as suits your circumstance.
  • Pair work, a book based activity to encourage co-operative learning. Modelling, especially when the concept of pair of group work is relatively new to a class, really sets the tone and promotes success. Choose a child to work with. Start the conversation:
    • I went first the last time, would you like to go first today?
    • Do you remember the first thing to do?
    • I think we roll the dice twice and add the numbers, do you agree?
    • Oh dear! Neither of us can remember what to do, will we quietly ask Tom?
    • Will you watch me while I’m taking my turn just in case I go wrong? I’ll help you too!
  • Stations: the organisation of these maths stations will depend on teaching style, the number of children, the ability level of the class and the assistance available from other staff members (SNAs, support teachers, etc.). And as with Pair Work it can take a little practice before the children approach stations successfully and productively – but it is well worth persevering! Station work promotes problem solving skills, group think and independence.The suggested stations can adapted in a number of ways:
    • use with similar ability groups or mixed ability
    • set up the activities at designated maths stations (tables or areas) which the class can rotate around eg 4 groups with 7 or 8 children per group; each group does two stations for 15 mins each for one class (30 mins total) and does the other two stations on the following day.
    • Each group does a station for one class, with each group working at each station over the course of the week.
    • Use the stations as a whole class activity e.g. on Monday all the class do the activities for station 1, on Tuesday do the activities for stations 2 etc. This does depend on there being enough of the required materials for the whole class to use them at the same time.
  • Books: Bearing in mind that Operation Maths is based on a CPA approach, it is envisaged that the child would engage in all the concrete and pictorial activities for the topic before doing the pages in their At School and At Home books. Furthermore, sometimes it is envisaged that the concrete activities for the topic at hand will take place during one week, followed by the book activities in the subsequent week (this will be explained in a paragraph under the Activities heading in the weekly plan in the TRB). If you are teaching in a multi-class situation, it would be better to stagger/alternate these weeks among the classes eg Week 1, first class do the concrete activities while second class are mainly book based; week 2, second class do the concrete activities while first class are mainly book based.

2. You don’t have to do it all!

In the junior end TRBs,  the plans are laid out in fortnights which then break-down into weekly suggested activities. The important word here is “suggested”; you are not expected to do everything, so pick and choose the activities that are most suitable for you, your children, the physical limitations of your class and/or equipment, the availability of support personnel. For example there are Aistear-linked themes and activities in the infant TRBs, but if these don’t appeal to you, or are not practical in your specific situation, ignore them.

As explained earlier, there are regular suggestions for stations in the first and second TRBs and in places in the infant TRBs, but again if you don’t have available colleagues (eg L/S Resource teachers, SNAs etc) to help with the running of these stations, then they probably are not for you. However, you could take one or two of the station activities and instead do it with the whole class as the same time. The choice is up to you.

3. MWBs! MWBs! MWBs!

I can’t stress how fabulously adaptable are the free mini-whiteboards or how they can make getting through content so much easier. I was using them for many years before the inception of Operation Maths and found them to be an invaluable tool in the classroom. Some of the ways in which they can be used:

Give Doodle Time! The temptation to doodle is overwhelming so spare a couple of minutes for a quick doodle or two! Signal the end of doodle time with a fun rhyme such as “Rub, a dub, dub! Give your whiteboard a scrub!”

Display the ebook on your IWB for Write-Hide-Show: This works very well as the children are not looking down at their own books, only up at the board, so it’s easier for teacher to check that they are focused on the task. Highlight a specific calculation on the ebook eg 16 + 5 and ask the children to write the answer on their MWBs, hide it (place it face down on the desk, or hold it face in, to their chest) while the other pupils are afforded thinking time and finally on a specific signal (eg aon, dó, trí, taispeán dom) all the answers are revealed simultaneously. Thus, the teacher can quickly assess the accuracy of the answers and allow this feedback to inform whether the class are ready to move on, or need more reinforcement.

“Show your thinking” The children can use quick jottings to explain how they arrived at a certain answer. The MWBs are less structured and easier to use than maths copies and easier to change if you want to amend your ideas. Interesting responses or approaches could easily be brought up to the top of the class for further discussion and display. Again, encourage the growth mindset; mistakes and multiple correct answers are opportunities to learn more.

More maths done in less time. Rooting in bags, finding their book, pencil, rubber… this all leads to a delay in actually getting down to the maths at hand. Whereas, just writing on the MWBs is much quicker and gets more done. And don’t worry if the associated page in the pupils book is not completed; remember the teacher’s aim should be to enable the children to achieve a certain objective/learning outcome and however that is achieved still counts, book or otherwise.

Step-by-step to show algorithms: if you are teaching some of the standard algorithms (eg column method addition or subtraction in first and second class) the MWBs can be handy to allow the teacher and class to do it together, step-by-step, with the children holding up their MWBs at every suitable juncture to check what they have done to that point. This way, potential mistakes may be picked up quicker and addressed before they begin to occur repeatedly.

4. Reduce your preparation

The plans are all done for you, the stations are all explained, the ideas are all there! This should significantly reduce the amount of time you were spending on maths preparation. However, it is still recommended to take the time at the beginning of each fortnight to go through the TRB and familiarise yourself with the content and the activities; this is time well spend that will translate into smooth running maths classes during the fortnight. But also be flexible, and don’t stick rigidly to everything.

One of the sections in the TRB where flexibility is advantageous is the photocopiables. There is a fantastic suite of resources here with great ideas, but don’t feel that if you don’t have 30 copies done in advance that you can’t use them. One example of this are the Yahtzee photocopiables in the TRB of Operation Maths 1. The children could simply write the target numbers ( eg 2-10, 2-20 or 0-5) on their whiteboards and cross them off when rolled. This also allows the game to be played repeatedly without needing other photocopies.

The one set of photocopies to have ready in advance are the Early Finishers and the Problem-Solving photocopiables. Initially, at the beginning of the school year, try to gauge how many copies you will need;you will probably not require 1 per child. As time goes on the number of copies of each can be adjusted, as necessary. These can then be kept near at hand to distribute to children in need of a more challenging or stimulating task.

5. Go digital!

The excellent suite of  digital resources available on Edco Learning can also aid efficient progress through content. The resources are very visual and help the child grasp a solid understanding of the concepts at hand quicker than might have occurred  otherwise. The resources can all be accessed directly via the hyperlinks in the digital books and it can be beneficial to have these tabs open in advance so as to save time during maths class. For more information on the extensive range of digital resources read on here

Teaching 3rd to 6th class? Read on to find out how to manage the content for those classes. 

Operation Maths – Improving standardised test scores?

Tags :

Category : About Operation Maths

Two days after the maths standardised tests were done in our school, a teacher on my staff came to me to let me know that 18 children in her room had gone up by a STen of 1 or more, a fact she was attributing to Operation Maths, which was being used throughout the school for the first time, since the previous September.

This information made me curious to see were there similar results in other class levels; below is a summary table of my findings:

Average Percentile for each class level, current and previous years in Drumcondra Primary Mathematics Test – Revised (DPMT-R):

Current Class 2012 2013 2014 2015 2016 2017 Difference 2016 to 2017
2nd 55 61 +6 PR
3rd 63 61 77 +16 PR
4th 66 61 70 79 +9 PR
5th 63 61 58 68 68 +0 PR
6th 42 53 73 75 75 75 +0 PR

These results only include the classes that had a previous DPMT-R to which a comparison could be made. Also, they are the average of all the children’s results that completed the tests in each year, therefore other variables like children of different ability joining or leaving the school hasn’t been accounted for. However, they do make for interesting reading, while also raising interesting questions:

  • 2nd, 3rd and 4th have made significant jumps, (3rd class in particular); could this be accredited to the Operation Maths programme (there were no other new initiatives this past year due to the freeze on the SIP for numeracy as directed by our union)?
  • 5th and 6th classes stayed the same; why wasn’t the programme as effective for these classes? In the case of this school, perhaps the scores being already quite high in those classes meant there was little room for improvement. Or perhaps, because Operation Maths is a radically different programme, one that requires an openness to change the way we think about maths, it has more impact on younger classes where the children are more malleable and less rigid in their way of thinking than some of the older students. If this is the case, could we then expect to see improved results also for 5th and 6th class students in the future when they have been using the programme from 2nd and 3rd class?

 

Of course, this is only a small insight into one school’s experiences, and to have more conclusive results, data would need to be collected from a wider range of schools and this data would need to be monitored over time to see if these results were maintained. However, it does raise some interesting questions, and does indeed appear to indicate tentative evidence that Operation Maths can have a positive impact on the standardised test scores of all the children in a class. That said, improving test scores was never the main goal of Operation Maths, rather the aim is for the children to understand maths, not just do maths.  And if standardised test scores increase simultaneously, then that indeed is a positive bonus!

Did you use Operation Maths for the first time this year? Have you seen any similar trends with classes in your school? Please share with us!

Post script: Some may also suggest that Operation Maths has question items that better prepare the children for those in the test (i.e. teaching to the test). Having deliberately tried to be as unfamiliar as possible with the  DPMT-R test when authoring Operation Maths, means I can’t comment either way as I just don’t know if the question items resemble test items. Personally, I have no experience of the SigmaT at all, and at the time of authoring Operation Maths,  the only DPMT-R that I had administered in the previous 6-8 years was the DPMT-R for 5th class.

 

Number Talks & Operation Maths

Tags :

Category : About Operation Maths

“The practice of number talks is one of the most powerful vehicles I know for helping students learn to reason with numbers and make mathematically convincing arguments, for building a solid foundation for algebraic reasoning, and for teaching mathematics as a sensemaking process. If all teachers make this shift in their practice, it would represent a profound advancement in mathematics education.”
Ruth Parker, co-author of  Making Number Talks Matter

As mentioned in a previous post, one of the mathematical pedagogies currently generating significant excitement is that of number talks. The buzz in maths education circles is all about developing number sense and number talks is being seen as one of the most powerful ways to enable this.

Here in Ireland, although the Professional Development Service for Teachers (PDST) has advocated the use of number talks in the PDST Mental Maths workshops and supporting manuals, and the more recent PDST Number Sense workshops, number talks is still relatively unknown. Similarly, there is very little in most of the maths text books available here, which explicitly promotes the development of specific mental maths strategies.

Not so Operation Maths. The promotion of the development of number sense is a key principle of the Operation Maths programme, as is the explicit exposure to a wide range of mental calculation strategies, most of which are also specified in the number talks approaches.

In this post, the connections between both number talks and Operations Maths will be shown, while also outlining how Operation Maths is the best programme to support the introduction and use of number talks in Irish classrooms. To read more about number talks generally, and access a whole suite of supporting resources  for all classes across the school,  please click here. To find out more about how Operation Maths works so well with number talks, please read on.

What does a Number Talk look like?

One of the definitive number talks texts is Sherry Parrish’s book Number Talks: Helping Children Build Mental Math and Computation Strategies, Grades K-5. In this book, she recommends the following structure:

Number Talks Approach

Operation Maths & Number Talks
1. The teacher presents a number sentence to the class; the students are given thinking time to mentally solve it. The horizontal number sentences in Operation Maths can in themselves inspire or be used as the basis for a number talk. For example, similar number sentences to the ones shown below this table were used to encourage the children to use compensation to solve calculations.
2. The students start with one fist to their chest;  they make a “thumbs-up” on their chest to show that they have found an answer. They then use the remaining time to try to think of another way/strategy which they then indicate by putting up a thumb and a finger, and so on. While I initially used this “fist and thumbs-up” system when collecting answers, after multiple times hearing “I had the same answer as Jack/Jill”, I returned to my preferred tool of using the Operation Maths mini-whiteboards, (to maximise on participation and honesty regarding answers).  It is important to insist that the MWBs are not to be used at all for working out, all of which is to happen in the heads, rather they should only be used to record the answer(s).
3. The teacher asks a number of children to volunteer their answers and all given answers are recorded on the board.
4. The teacher asks a child to “defend their answer”/”explain their strategy”. For the children to explain clearly, they need to have the correct mathematical language so that all listeners can follow their thinking. Thus, children who have been using the Operation Maths programme are typically better able to express their thinking using the correct mathematical language and terminology that is being emphasised throughout these books.
5. All strategies are recorded on board by teacher, using visuals where possible to make the strategy less abstract for the other listeners. Many of the visual strategies that are specifically recommended to be used are ones that already used extensively throughout Operation Maths eg frames, empty number lines, bar models (referred to as part/whole models), arrays and  area models. Branching is another visual way to demonstrate strategies particularly when partitioning (breaking into place value parts) /or compensation is involved.
6. The children agree on the “real” answer. Depending on the range of possible answers given, the children can also be asked to identify any unreasonable answer from those suggested and explain why they think so. This in turn encourages them to apply the variety of estimation strategies taught in the Operation Maths programme
These actual number sentences or similar ones could be used as the basis for a number talks session (from Operation Maths 1)

Other ways in which Operation Maths and Number Talks work so well together:

  • In the junior end of the school, number talks is very much about the children developing their ability to conceptually subitise  (i.e. to recognise that there is 8 counters because there is a group of  5 and a group of 3) using a variety of images, including five and ten frames. Operation Maths also recognises the value of using frames throughout the programme in Junior Infants to Second class and provides these frames as part of the pupils’ book packs in these classes, as well as having digital eManipulatives  (i.e. the Sorting eManipulative) to support their use.
  • In Sherry Parrish’s book Number Talks: Helping Children Build Mental Math and Computation Strategies, Grades K-5, she lists a whole range of specific strategies for the four operations, almost all of which are also explicitly taught or emphasized in the Operation Maths programme, including the strategy of compensation. To see an overview of the number talks strategies and where they overlap with Operation Maths click this link: Strategies in Number Talks & Operation Maths
  • For those teachers using Operation Maths, they are already familiar with the structure of having an oral and mental starter at the beginning of each maths lesson. Number talks can be used interchangeable with the starters in the Operation Maths starters bank so as to add further variety to lessons.
  • The strong emphasis on talk and discussion ( eg Talk Time in the pupils books, discussion and questions given in the TRBs) in Operation Maths further supports number talks as it prepares the children for situations in which they will be asked to explain their reasoning.

So there you have it, Number Talks & Operation Maths: a perfect partnership for each other!

Are you compensating?!

Tags :

Category : About Operation Maths

A key recurrent theme in Operation Maths is the teaching of specific strategies to promote the development of flexible and fluent mathematical learners. In a similar way to the Building Bridges approach to reading, which advocates explicitly teaching specific reading comprehension skills, Operation Maths explicitly explores a range of specific strategies in a spiral and progressive way, in order to equip the children with the necessary skills for them to become capable and confident at problem-solving and computing mentally. Particular to mental computation, Operation Maths introduces the children to a range of of mental calculation skills, one of which is compensation.

 

Compensation

 

Compensation is primarily an addition strategy where the aim is to to adjust one addend to become an easier number to add with.  This involves moving the quantity required to do this  from one addend to the other. In Operation Maths, these easier numbers are usually referred to as  friendly or compatible numbers and can include doubles, multiples of ten (10, 20, 30…) or, in the older classes, multiples of the powers of ten (100, 200, 300…..; 4,000,  5,000,  6,000 etc).

 

Concrete

As with all new concepts and strategies, Operation Maths advocates a CPA approach. An ideal introduction to compensation is with the Operation Maths frames in first class when the children first begin to notice how adding onto 9 can be made easier by moving a counter from the other quantity to the 9 to make it become a ten. When ready, the children can also begin to explore how they can also make tens when adding to 8 and 7 by moving 2 and 3 counters respectively.

This can progress to using cubes  for bigger numbers; again, this should start with addends ending in 9 eg 19, 29, 39 etc. Encourage the children to see ways to make the calculations become easier, and encourage them to use the language of moving (not adding or subtracting) a cube from one number to the other, to make a friendly number. When ready, they should then develop this strategy to use with addends ending in 8 and 7, by moving 2 and 3 from the other number. In this way, the children can also begin to start doing addition with renaming, without having to grapple with the traditional written algorithm ( or column method).

Pictorial

With first and second classes, it can be helpful also to show what is happening to the actual numbers in the calculation by using an arrow to highlight the quantity moving from one addend to the other. Notice how the calculation is being presented horizontally; this encourages children to consider the whole number and how it relates to the other number in the calculation. It also encourages the child to consider alternatives to the written column method, on which many children can be over-reliant.

In the senior end books for Operation Maths, branching (see red figures below) is used  to show the process of compensation and this can be particularly useful when the numbers involved are bigger than what might practically be shown using concrete materials. Never-the-less, it is always recommended to return to examples that can be demonstrated concretely, if the child finds the intermediary branching stage difficult to understand.

Abstract

The ultimate aim is, that when presented with a random calculation, that the children will recognize and use compensation if it is an appropriate and efficient strategy. The suitability of compensation as an efficient strategy will depend on the numbers involved, which in turn requires flexibility on the child’s part. In most cases, this will only be likely, if they have previously encountered compensation, and a variety of other mental computation strategies, in structured  and meaningful lessons, like those provided by Operation Maths.

 

Further reading:

 

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